Eastwards means towards the east. It is almost the same as eastward, but it is used as an adverb: it tells you which way something moves or looks — we drove eastwards; the land falls eastwards to the sea. British English likes eastwards a little more than American English does. You will not often hear “an eastwards train”; people say an eastbound train or an eastward journey instead. So the extra s does not make a new meaning. It is only a slightly different coat on the same direction word. In everyday talk, go east is still the simplest. Use eastwards when you want that “moving in that direction” feel, not when you mean a person from the east, and not when you mean the furthest east point.